The length of the latus rectum of the parabola $y^2+8x-2y+17=0$ is

$A$ quadratic polynomial $y = f(x)$ with absolute term $3$ neither touches nor intersects the abscissa axis and is symmetric about the line $x = 1$. The coefficient of the leading term of the polynomial is unity. $A$ point $A(x_1, y_1)$ with abscissa $x_1 = 1$ and a point $B(x_2, y_2)$ with ordinate $y_2 = 11$ are given in a Cartesian rectangular system of coordinates $OXY$ in the first quadrant on the curve $y = f(x)$,where $O$ is the origin. The graph of $y = f(x)$ represents a parabola whose focus has the coordinates:

The point at which the line $y = mx + c$ touches the parabola $y^2 = 4ax$ is

$\triangle OAB$ is an equilateral triangle inscribed in the parabola $y^2 = 4ax, a > 0$ with $O$ as the vertex. Then the length of the side of $\triangle OAB$ is

What are the parametric equations of the parabola $(y - 2)^2 = 12(x - 4)$?

The point on the axis of the parabola $3y^2+4y-6x+8=0$ from which $3$ real normals can be drawn is given by: